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I also have the same issue on an LG Smart TV. Episode 4 of Grand Tour works, along with other content in the amazon prime video app, however for episode 5 of Grand Tour, I get an insufficient bandwidth error. No other devices connected to the wifi or internet, 180Mbps+ download speed.
I uninstalled and reinstalled my prime video app, did not do anything to resolve the problem. I can load the episode on my computer with no issue, but I wish to watch it on the larger screen. Tried connecting my computer via HDMI to my smart TV but amazon prime would not allow it. Said something to the effect that not all the devices were HDCP compliant. The TV is an LG webOS TV UH7650.
All the software on the TV is up to date. This seems like an issue with amazon and perhaps LG TVs as I have seen similar issues in other forums with the insufficient bandwidth message on LG smart TVs.
So, I've attempted a few things and still have the same issue:
Router updates, Hub/Switch removal
Hardline Fibre Modem straight into TV, ran ookla speedtest at 150 Down / 125 Up (on the tv itself).
Samsung TV Refresh App install etc...
The actual Amazon Prime Video App was refreshed as was the TV and it appears this is the only App on my TV to have the issue, and mainly with 4k HDR content.
All other titles work for me, but I tried "The Expanse" and it also came up with insufficient bandwidth. Was this just added to Prime around the same time as Episode 5 of Grand Tour (S3)?
All Prime Video shows and movies take far longer to up the resolution than my other streaming services, Youtube and Netflix seem to instantaneously load in full 4k without delay and the picture quality never lags but ever since a few days, Amazon is very slow to up the quality as it loads...
On my Computer/Phone etc it loads lightning quick without issue.